Figure shows three oscillating LC circuit with identical inductors and capacitors.If `t_(1),t_(2), t_(3)` are the time taken by the circuits I, II, III for fully discharge, then

Options

A. `t_(1) gt t_(2) gt t_(3)`
B. `t_(1) lt t_(2) lt t_(3)`
C. `t_(2) lt t_(1) lt t_(3)`
D. `t_(3) = sqrt(t_(1)t_(2))`

Answer

C

Explanation

Time period, `T_(1) = 2pi sqrt(LC), T_(2) = 2pi sqrt((LC)/(2)),T_(3) = 2pi sqrt(2LC)`.
Clearly `t_(2) lt t_(1) lt t_(3)`.